Block #2,757,565

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/20/2018, 2:19:58 PM · Difficulty 11.6661 · 4,073,483 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

397834bd8467989e6a653e86b220464c17df85c47a3df439c08d784279599b5d

View on Chainz ↗

Height

#2,757,565

Difficulty

11.666086

Transactions

Size

1.22 KB

Version

Bits

0baa849b

Nonce

178,447,817

Timestamp

7/20/2018, 2:19:58 PM

Confirmations

4,073,483

Mined by

⛏️ P2SHAGoBRrpS8wLcwWcjH2ht5P8drXsfheZXDn

Merkle Root

06808ceed55d74c877621f44ce2d89d7fcbcaae491efe2f55a3e8e8d2c5f8f98

Transactions (3)

Coinbased053957eccf705…9806516bf3c49b

1 in → 1 out7.3600 XPM110 B

AGoBRrpS…sfheZXDn

d993046cb221c1…df3cb0decf2cb7

3 in → 2 out503.6468 XPM523 B

AaoVyS59…FvfsDsDv APyiuUwp…Dtu7RVMZ

057764448dbdfa…007f60ffead262

3 in → 2 out40.0100 XPM522 B

AaoVyS59…FvfsDsDv AejbeLty…Nt1sjUp6

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.983 × 10⁹⁴(95-digit number)

99835734228879521081…38764598958924557439

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

9.983 × 10⁹⁴(95-digit number)

99835734228879521081…38764598958924557439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.983 × 10⁹⁴(95-digit number)

99835734228879521081…38764598958924557441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.996 × 10⁹⁵(96-digit number)

19967146845775904216…77529197917849114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.996 × 10⁹⁵(96-digit number)

19967146845775904216…77529197917849114881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.993 × 10⁹⁵(96-digit number)

39934293691551808432…55058395835698229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.993 × 10⁹⁵(96-digit number)

39934293691551808432…55058395835698229761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.986 × 10⁹⁵(96-digit number)

79868587383103616865…10116791671396459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.986 × 10⁹⁵(96-digit number)

79868587383103616865…10116791671396459521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.597 × 10⁹⁶(97-digit number)

15973717476620723373…20233583342792919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.597 × 10⁹⁶(97-digit number)

15973717476620723373…20233583342792919041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.194 × 10⁹⁶(97-digit number)

31947434953241446746…40467166685585838079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #2,757,565

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